Isomorphous_replacement
Isomorphous replacement (IR) is historically the most common approach to solving the phase problem in X-ray crystallography studies of proteins. For protein crystals this method is conducted by soaking the crystal of a sample to be analyzed with a heavy atom solution or co-crystallization with the heavy atom. The addition of the heavy atom (or ion) to the structure should not affect the crystal formation or unit cell dimensions in comparison to its native form, hence, they should be isomorphic.
Data sets from the native and heavy-atom derivative of the sample are first collected. Then the interpretation of the Patterson difference map reveals the heavy atom's location in the unit cell. This allows both the amplitude and the phase of the heavy-atom contribution to be determined. Since the structure factor of the heavy atom derivative (Fph) of the crystal is the vector sum of the lone heavy atom (Fh) and the native crystal (Fp) then the phase of the native Fp and Fph vectors can be solved geometrically.
The most common form is multiple isomorphous replacement (MIR), which uses at least two isomorphous derivatives. Single isomorphous replacement is possible, but gives an ambiguious result with two possible phases; density modification is required to resolve the ambiguity. There are also forms that also take into account the anomalous X-ray scattering of the soaked heavy atoms, called MIRAS and SIRAS respectively.[1][2]